I initially made Lauren as a sister to a character called Kate. But Lauren turned out to be far more interesting than her sister so I chose to scrap Kate and have Lauren as a character.
Lauren has been a part of three TES games and will most likely move away from Skyrim to experience [insert TES VI province here].
Considering she lives practically forever, she chooses to enjoy the moment because her followers/wive/husband won't follow her into the next life (except for Vilja who also found the eternal youth secret).
Yes, it does.
Though with Lauren, I do the opposite. In Oblivion, she's gimped but in Morrowind and Skyrim, she brings over her money, basic weapon and clothes from the other lands